Software Quality Assurance & Testing
Software Quality Assurance involves the entire software development PROCESS - monitoring and improving the process, making sure that any agreed-upon standards and procedures are followed, and ensuring that problems are found and dealt with. It is oriented to 'prevention'.
Software Testing involves operation of a system or application under controlled conditions and evaluating the results (e.g. 'if the user is in interface A of the application while using hardware B, and does C, then D should happen'). The controlled conditions should include both normal and abnormal conditions. Testing should intentionally attempt to make things go wrong to determine if things happen when they shouldn't or things don't happen when they should. It is oriented to 'detection'.
Source:http://www.softwareqatest.com/qatfaq1.html#FAQ1_1
Also See:
Difference between Quality Control & Quality Assurance